11 ms·
The tyranny of the wagon equation
- mabbo 4y agoThe author misses a key important point: you can also eat the donkey.
- 988747 4y agoBut you can't feed the donkey to remaining donkeys.
- progre 4y agoI'v seen donkeys happily munching down plastic bags and cardboard. I sure you could feed dried donkey meat to a donkey (not saying it's a good idea)
- 988747 4y agoAnd the effect for a donkey would be probably similar to eating plastic bags: They cannot properly digest it so they suffer from malnutrition, eventually die.
- zardo 4y agoThat would certainly extend your range, but it would be very costly in donkeys. Instead of needing 1000 donkeys to sustain a siege, you now need say 100 donkeys/day.
- motohagiography 4y agoYou can also breed them (though you can't breed mules without horses, etc). There is a cycle in this equation where you can breed replenishment donkeys once from a subset of them every year or so, and they go into productive use after about 2-3 years. Depending on the length of your campaign, you can extend your range by eating older donkeys as jerky and soup and breeding new ones. Setting out with a bunch of pregnant donkeys could also extend your range and campaign. Add goats (who can even ride donkeys) and you have a renewable source of protein via milk and cheeses. Horse gestation is marginally shorter, but you can also milk them to feed troops, as mogolians did. I don't know if you can milk donkeys, and mules less likely given their sterility. This is complex enough that it could become a game.
- _vdpp 4y ago“Harmonic Donkey Transfer” would be a good band name or album title.
- Animats 4y agoCaravans faced this problem, but the solution was commercial - the caravanserai. A serai is a corral for animals. A caravanserai is a truck stop - fuel, food, motel, parking. Caravans resupplied at caravanserai. The Silk Road was a chain of caravanserai. If there's enough local production to supply a caravanserai, caravans can take that route. The military version of this is a chain of supply bases. This is all too common. A gallon of diesel fuel delivered by the US military to outermost bases in Afghanistan could cost well over US$100. Part of the trip was made by transport aircraft, and part by helicopter, all of it consuming fuel. Bases have to be within helicopter range of each other. The main justification for the Osprey, which is a horrible kludge of an aircraft, is more range, allowing fewer bases to reach a goal.
- schoen 4y ago> If there's enough local production to supply a caravanserai, caravans can take that route. That's an interesting constraint; were there also extra-expensive caravanserai in places where that production wasn't quite local and some of those resources had to be trucked, er, caravanned in?
- samatman 4y agoSort of, mostly yes, but never fodder or water. This is the great advantage of the camel: if a camel train rolls into a caravanserai, and the available fodder at that oasis has been eaten, there's a good change they'll make it to the next oasis with thin, very unhappy, camels. Mules would just die.
- csours 4y agoI had heard of caravanserai from the idle/progression Kittens Game. I wish I had looked it up earlier.
- JJMcJ 4y agoBy no means an expert but my understanding is that if you can't make the logistics work for a military operation then the chances of failure are very high, maybe even literally 100%.
- zardo 4y agoTo make this map to the real world, terrain must be taken into account. Obviously donkeys can haul more weight over more distance on flat ground than climbing a mountain pass. What's the approach to doing that? Make the delta and v terms functions of the terrain? Re-derive the equation based on energy rather than distance?
- smallnamespace 4y agoEven easier: redefine distance, e.g. 1 mountain mile = 5 flat ground miles
- Sniffnoy 4y agoThis is known in mathematics as the Jeep problem: https://en.wikipedia.org/wiki/Jeep_problem https://en.wikipedia.org/wiki/Jeep_problem
- superjan 4y agoIn university, my colleague students were developing strategies to the “camel banana problem” for transporting n bananas by camel into the desert. https://puzzling.stackexchange.com/questions/230/a-camel-transporting-bananas https://puzzling.stackexchange.com/questions/230/a-camel-tra...
- motohagiography 4y agoIn an amazing thread about an amazing article, as a Jeep owner, I did not know about this. It's like the bumper stickers print themselves. However I suspect that given their fuel consumption, owning a Jeep itself may be proof someone does not understand this problem.
- nvader 4y agoBring war material with you from home, but forage on the enemy. Thus the army will have food enough for its needs. --Sun Tzu, The Art of War
- mcguire 4y agoIt works well enough to be a consistent strategy, but you have to be careful taking too much from a given piece of territory. Eventually, the locals start getting unhappy with you. And then there's things like the Thirty Years' War, where armies foraged their way through territories often enough that eventually there was nothing left.
- zardo 4y ago> Eventually, the locals start getting unhappy with you. Pretty sure the locals are unhappy from the start of the foraging process, with all the stealing, murdering, and raping.
- pessimizer 4y agoUnhappy is being used here to mean "unhappy enough that it affects you." It's not about concern for the mental health of the locals.
- mcguire 4y agoThere is more than one way to forage. At best, the army can pay the local inhabitants, maybe even a fair value, particularly if the area is nominally friendly. Even if the army "commandeers" supplies, it would want to keep the criminal activity to a minimum, if only because it is bad for discipline. The Thirty Years' War is an extreme case, in large part because the armies were made up of mercenaries that were not getting paid regularly.
- watwut 4y agoI think that with Thirty Years' War, it was not just "foraging"bur also religious cleansing. It was kind of genocide. They did not had word genocide yet, but generally it fits.
- JAA1337 4y ago
- csense 4y agoOnce your nation gets big enough, you can't supply frontier armies from the capital. You need to draw food from local sources. In territory you control, the peasants pay some of their food to the local fortress in taxes, and the fortress acts as a supply base for any army that needs to go through. Once you get past border action and deep into enemy territory, the tyranny of the wagon equation means it's down to "forage" -- hunt / fish / gather resources from the wild, or steal food from the local population at swordpoint. One option is to pause your campaign until you can consolidate your gains and build or take over supply bases in captured territory. Another option is to change your tactics to recognize the limits of what a foraging army can achieve. E.g. avoiding sieges and terrorizing civilians / burning towns to try to force a surrender, or using a cavalry army or fast-moving elite infantry to launch a surprise attack in an unexpected location.
- chmod600 4y agoI read that Ghengis Khan did much better by making good use of grazing lands and timing the seasons.
- brazzy 4y agoYes - but that meant his entire army had to be cavalry, and could basically only operate on steppe-like land.
- deepnotderp 4y agoA better analogy would be the Breguet range equation, as the rocket equation is explicitly about delta-V, not distance. https://aerospaceengineeringblog.com/breguet-range-equation/ https://aerospaceengineeringblog.com/breguet-range-equation/
- andrewf 4y agoReminds me of that time the RAF really wanted to drop some bombs on the Falkland Islands rather than leaving it to the Navy and its Sea Harriers. Diagram: https://en.wikipedia.org/wiki/File:Refuelling.plan.black.buck.svg https://en.wikipedia.org/wiki/File:Refuelling.plan.black.buc... Full article: https://en.wikipedia.org/wiki/Operation_Black_Buck https://en.wikipedia.org/wiki/Operation_Black_Buck
- ticviking 4y agoIn an acquaintances DnD game he often enforces encumbrance and logistics rules like this. Leading the players to realize, "this plan requires infinite donkeys doesn't it?"
- tus666 4y agoThere is another kind of tyranny equation - the steam locomotive going up an incline. Essentially the problem is the power output of the engine is locked into step with the speed of the wheels - the slower you go, less pushes of the pistons, less power. So as a steam train starts up an incline, it will start to decelerate, causing it to produce less power, causing it to slow even further and so on. A true vicious cycle. This was one of many benefits of diesel-electric locomotives - the engine speed (hence power) was decoupled from the train speed.
- jeeeb 4y agoICEs have the same problem though. If they don’t rotate fast enough they stall. For ICEs we solve the problem with gear boxes. Couldn’t the same solution have been used for steam engines?
- tus666 4y agoThey did exist but were not common: https://en.wikipedia.org/wiki/Geared_steam_locomotive https://en.wikipedia.org/wiki/Geared_steam_locomotive
- emtel 4y agoI don’t think that explanation is correct. The torque curve of a steam engine peaks at 0rpm and slopes down from there. The engine is simply decelerating to the point where it’s torque is balanced with the force of gravity on the incline.
- tus666 4y agoIt has no choice but to decelerate, as the train itself will decelerate up an incline (without increasing power), and they are coupled. And yes the torque balance is why steam trains could climb gentle gradients at all. However the loss of power due to fewer piston pushes means that the peak 0rpm is reached very quickly. Diesel electric locos can literally increase RPM and power as they start to climb the gradient, with no connection between the slowing train speed and engine power.
- eternalban 4y agoThose donkeys in the first pic look so happy. "WFH!"
- credit_guy 4y agoA way to solve the wagon equation is to build really good roads. Which is what the Romans did. Maybe that was their secret sauce.
- h2odragon 4y ago> Thus, the harmonic donkey transfer, using four donkeys, yields a maximum transport distance 1/12 * L0 longer than the pairwise donkey transfer. Upvote earned there.
- moron4hire 4y agoWithout digging into any math myself, I find it curious that it's 1/12th longer. That specific ratio, 1/12th, is also the basis for the Equal Temperament system for tuning Western musical instruments ("12-tone Equal Temperament, specifically), which also represents a harmonic series. https://en.wikipedia.org/wiki/Equal_temperament https://en.wikipedia.org/wiki/Equal_temperament
- oakwhiz 4y ago1+2+3+...=-1/12 by certain definitions...
- sparkplug94 4y agoHaha thank you! I'm the original author of the linked article, and I had a LOT of fun naming the donkey transfer algorithms I came up with.
- deleted 4y ago[deleted]
- vitiral 4y agoFunny. However, I find some assumptions suspect. Unlike rockets, donkeys can consume fuel en-route by grazing. Armies can also consume fuel by hunting, plundering and being "quartered" by their own people. You can make "supply trains" by having small groups of military gather such resources from a closer distance. This is probably fairly accurate for camels and distances in the Saharan desert though, and you'd have to add the weight of water as well!
- igorkraw 4y agoThe linked source blog goes into that: - grazing costs time, which increases the total amount of food that must be carried - foraging equally costs time, so foraging more means a slower moving army - but an army can only forage as it passes through terrain, so you need to keep moving, otherwise your army will eat the area into starvation, then die
- Retric 4y agoIt’s not quite that simple. Horses can eat much faster than they can digest so a few short breaks can represent a lot of food over a day. Further, horses eat significantly more than people. A 30% slower pace that requires 40% less food per day is a net win on distance but not time.
- throwawayffffas 4y agoThe main issue, is that the horses of agricultural societies are bred to a large size, and cannot survive by grazing alone, they need to have grains in their diet.
- Retric 4y agoThat’s false. Horses doing heavy work can’t survive on grazing alone, but they are perfectly fine when left alone in good pasture. Thus the phrase “put out to pasture,” old animals where often given something of a retirement where they where left to take care of themselves rather than simply be killed.
- ballenf 4y agoOne commenter questions whether generals and armies were capable of the advanced math implicated by the harmonic transfer method. But they don't have to do any advanced math. They just take food for the fleet from a single donkey and turn that donkey around as soon as his food supply equals the food necessary for the return trip. Rinse and repeat. Right? The reality does get a bit more complicated because at least one guide is required for each donkey, so you really don't want to lose a man for every donkey that turns back, and instead do the maneuver in groups. You also need to feed the return guide. Optimizing under those conditions gets a lot more complicated I think. You could also use this logic for sherpa-assisted mountain climbing.
- jerf 4y agoThis analysis also quite reasonably assumes zero transfer time between donkeys, perfect knowledge to run donkeys to exactly their limit (which are identical between all donkeys), and zero overhead in general. That's all fine, it's an upper limit analysis. But the overhead will be biting you in the exponential regime, unfortunately. Another thing to remember about "the old days" is that they may not have computers and they may not have the Internet, but they have LOTS of time to think about more efficiency compared to an Internet commenter for whom this is merely a momentary side diversion for a few moments, and a lot more motivation. I feel satisfied with some of the answers to things like "How was Stonehenge built?" that have been found in the last couple of decades (or, if you prefer, "Can you show at least one method that could have been used to build Stonehenge?"), but I think one of the other lessons that was learned (at least by me) is that "take a modern person, give them one try in their busy lives to try the first thing that comes to their mind, and declare the task impossible when that doesn't work" isn't a very good way to understand the ancient world. They had time. Would an ancient have described the "harmonic transfer technique" in this way? Heck no. Could they have worked their way to it through trial, error, and much simpler thinking? Absolutely. Finding that solution doesn't require calculus. Calculus just supplies a very nice analysis framework and a fantastic communication tool between the post author and us readers.
- dylan604 4y ago>because at least one guide is required for each donkey, Why? Can you not assemble them in groups like other pack animals?
- crest 4y agoThis assumes that beasts of burden aren't edible...
- bombcar 4y agoThe underlying blog post (which is MUCH more detailed) goes into that (not sure which of the three went into it in detail) https://acoup.blog/2022/07/15/collections-logistics-how-did-they-do-it-part-i-the-problem/ https://acoup.blog/2022/07/15/collections-logistics-how-did-... There are problems with eating the beasts, but in certain cases it can extend your range, but not as much as you might think.
- endominus 4y agoThere's also an element of "burning the ships" in that idea; you extend your current operational range at the cost of the logistical capacity (in terms of carried food) of the future. In other words, if you eat all your horses and you're still behind enemy lines, your army is now in serious trouble of not being able plunder enough food to make it anywhere before starving and deserting.
- BizarroLand 4y agoTo add to that, we can, with our current technology, for a handful of billion dollars send a rocket to Andromeda that would arrive in 10,000 to 65,000 years. But if we want the rocket to be anything more than a pitted lump of metal when it arrives, say, sending information back, operating scanners, etc, the price jumps exponentially (assuming any useful technology we build could still be usable even after 100 years in deep space). It ultimately boils down not to the "Can we do it", but "Is it WISE to do it", and that is always either the more difficult or more expensive question to answer.
- credit_guy 4y ago> send a rocket to Andromeda that would arrive in 10,000 to 65,000 years Andromeda is 2.5 million light years away. You are probably thinking of sending some vehicle to the closest star, Proxima Centauri, which is just about 4.25 light years away. This is the same as 270000 AU away; Voyager 1 has been launched 45 years ago, and it's at 157 AU from Earth, which means it traveled at an average speed of about 3.5 AU/year. At this speed it would take it 77000 years to get to Proxima Centauri.
- dragontamer 4y agoThere is an escape from the donkey in practice. Its called a boat, which can scale as big as possible and supply any number of donkeys across the entirety of the Mediterranean.
- bee_rider 4y agoThe blog posts by Devereaux (acoup blog) that spurred this on, are specifically about over-land logistics. Boats, of course, avoid this problem entirely -- assuming all of your targets are coastal or by rivers!
- mellavora 4y agoas long as you are near the shore-line, I can see that working. Though you might also need to be near a port; loading/offloading is less efficient without infrastructure. However, there may be other uses for the port, which suggests most of the good ports will have cities built around them. So yes, as long as you constrain your march to the area around friendly cities, boats work great
- tomjen3 4y agoYou don't really need much infrastructure when you don't use containers for your boats.
- dragontamer 4y ago> as long as you are near the shore-line Look at Bronze / early Iron age Mediterranean empires. They stuck to the shorelines. https://en.wikipedia.org/wiki/Ancient_Carthage#/media/File:Carthage_Holdings.png https://en.wikipedia.org/wiki/Ancient_Carthage#/media/File:C... https://upload.wikimedia.org/wikipedia/commons/f/f7/Greek_Colonization_Archaic_Period.png https://upload.wikimedia.org/wikipedia/commons/f/f7/Greek_Co...
- marcosdumay 4y agoThey started moving inroad after they started making roads.
- photochemsyn 4y agoA text-based 'Oregon Trail'-style game could be built out of this concept, where the player starts with a fixed sum of money and has to buy enough donkeys and food, plus perhaps plan a route with optimal water and grazing potential, to reach their destination.
- cwmma 4y agoThe diagram of the Quadruple donkey transfer reminds me of the fueling diagram for the Black Buck raids during the Falklands War 1. https://en.wikipedia.org/wiki/Operation_Black_Buck#/media/File:Refuelling.plan.black.buck.svg https://en.wikipedia.org/wiki/Operation_Black_Buck#/media/Fi...
- sparkplug94 4y agoThat's actually shockingly similar. I'm sure someone has studied the mathematics of fuel transport in much greater detail -- I wonder if it's a simple problem to optimize or something closer to the traveling salesman problem
- cwmma 4y agopretty sure it's a very simple problem, brutally simple even.
- shalmanese 4y ago> “Hierarchy, Vorbis said later. The Ephebians didn't think in terms of hierarchies. > No army could cross the desert. But maybe a small army could get a quarter of the way, and leave a cache of water. And do that several times. And another small army could use part of that cache to go further, maybe reach halfway, and leave a cache. And another small army . . . > It had taken months. A third of the men had died, of heat and dehydration and wild animals and worse things, the worse things that the desert held . . . > You had to have a mind like Vorbis's to plan it. > And plan it early. Men were already dying in the desert before Brother Murduck went to preach; there was already a beaten track when the Omnian fleet burned in the bay before Ephebe. > You had to have a mind like Vorbis's to plan your retaliation before your attack.” - Small Gods, Terry Pratchett
- schoen 4y agoI thought "that's a funny coincidence with the Vorbis file format name!" ... but then I thought maybe it wasn't a coincidence at all. And it wasn't! https://en.wikipedia.org/wiki/Vorbis#Name https://en.wikipedia.org/wiki/Vorbis#Name